MAXLN - THE MAX LINES

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In this problem you will be given a half-circle. The half-circle’s radius is r. You can take any point A on the half-circle and draw 2 lines from the point to the two sides of the diameter(AB and AC). Let the sum of square of one line’s length and the other line’s length is s

Like in the figure s = AB2 + AC. And BC = 2r.

Now given r you have to find the maximum value of s. That is you have to find point A such that AB2 + AC is maximum.

Input

First line of the test case will be the number of test case T (1 ≤ T ≤ 1000). Then T lines follows. On each line you will find a integer number r (1 ≤ r ≤ 1000000); each representing the radius of the half-circle.

Output

For each input line, print a line containing "Case I: ", where I is the test case number and the maximum value of s. Print 2 digit after decimal (Errors should be less then .01).

Example

Sample Input:
1
1

Sample Output:
Case 1: 4.25

hide comments
rohitjv: 2012-02-11 10:59:38

take care of the data types......i costed me many errors

Jakub ©afin: 2012-01-02 19:32:58

Anyway, a testcase can be solved in constant time... the math behind it is nice and simple

fandi a rahadian: 2011-11-30 11:40:32

why im getting TLE? lol. what will make me TLE, anybody please help

MR. BEAN : 2011-10-19 13:46:15

simple differencial application!!!

magicsquare: 2011-10-19 08:41:28

tutorial for sure!

cc: 2011-10-10 16:08:41

for c++ users: use int for the test case, long long int for the radius, and double for the result :)

Nnavneetsinha: 2011-09-24 06:10:02

some mathematics needed only.
tutorial problem.

Last edit: 2011-09-24 06:10:31
manish kapoor: 2011-07-28 10:30:22

my code runs fine for d given test case ,pls give sm more test cases....pls (sm odd ones)

oldmonk: 2011-06-12 19:08:36

do some math to get value of AC.. :)

Last edit: 2011-06-12 19:09:02
Rohan Laishram: 2011-06-02 08:39:11

Tutorial


Added by:Muhammad Ridowan
Date:2011-03-28
Time limit:1s-1.679s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:Own Problem(used for CSE,University of Dhaka, Newbies Contest)